Question

A sugar solution was made by mixing 3 gal. of a 50% sugar solution and 9 gal. of a 30% sugar solution. Find the concentration of the new mixture.

Answer 1

The new mixture is acquired from the sum of the concentration divided by the total number of gallons. Or we could write it like this.
mix =
`\cfrac{\text{concentrate} * gallons+\text{concentrate} * gallons}{\text{the total number of gallons}}`

Input the numbers
mix =
`\cfrac{50 \% * 3+30 \% * 9}{3+9}`

simplify the dividend and divisor
mix =
`\cfrac{150 \%+270 \%}{12}`
mix =
`\cfrac{420 \%}{12}`
mix =
`\cfrac{420 \%}{12}`
mix = 35%

The new concentration is 35%